1. S. T. Joshi’s 704-page biography of Lovecraft does not include an index listing for Mencken. So it’s probably safe to say they didn’t meet.
2. As for economics, Lovecraft was a nominal Republican in the 1920s who went whole hog for socialism in the 1930s. According to Joshi, he advocated “government control of large accumulations of resources (including utilities) and their operation not on a basis of profit but strictly on need,” fewer working hours at higher pay, old-age pensions, etc. In 1932, Lovecraft probably would have voted for socialist candidate Norman Thomas, except that he thought it would have wasted his ballot. He backed the radical senatorial candidacy of Upton Sinclair in 1934. The next year, he said he favored something “considerably to the left of the New Deal.” In 1936, he said that FDR was “too subservient to capitalism.” Lovecraft died in 1937.